Answer:
1312 feet
Step-by-step explanation:
41 ft=1 sec
how about 32 sec
41 x 32=1312/1=1312
A large sample of men, aged 48 was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men 90% were alive at 65%. Is this a sample or population?
Enter the coordinates of the point on the unit circle at the given angle. 150 degrees. please help!
Answer:
[tex]\boxed{(-\frac{\sqrt{3}}{2}, \frac{1}{2})}[/tex]
Step-by-step explanation:
Method 1: Using a calculator instead of the unit circle
The unit circle gives coordinates pairs for the cos and sin values at a certain angle. Therefore, if an angle is given, use a calculator to evaluate the functions at cos(angle) and sin(angle).
Method 2: Using the unit circle
Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.
This coordinate pair is (-√3/2, 1/2).
Answer: This coordinate pair is (-√3/2, 1/2).
Step-by-step explanation:
Use the unit circle to locate the angle measure of 150° (or 5π/6 radians) and use the coordinate pair listed by the value.
Select the correct answer. Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing diameters of the circle. He labels the ends the diameters A, B, C, D, E, and F, and he uses a straightedge to draw the chords that form a hexagon. Which statement is true? A. Vincent’s construction method produces a hexagon that must be regular. B. Vincent’s construction method produces a hexagon that must be equilateral but may not be equiangular. C. Vincent’s construction method produces a hexagon that must be equiangular but may not be equilateral. D. Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
Answer:
B.
Step-by-step explanation:
Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular. The correct option is D.
What is a regular polygon?A regular polygon is a polygon that is equiangular and equilateral. Therefore, the measure of all the internal angles and the measure of all the sides of the polygon are equal to each other.
Given that Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing the diameters of the circle.
Now as it can be seen as the paper is folded as shown in the below image but it does not create a hexagon that is equilateral and equiangular.
Hence, Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
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The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v).
Estimate the values of fT(−15, 50) and fv(−15, 50).
V 20 30 40 50 60 70
T
−10 −18 −20 −21 −22 −23 −23
−15 −25 −26 −27 −29 −30 −30
−20 −30 −33 −34 −35 −36 −37
−25 −37 −39 −41 −42 −43 −44
Answer:
value of Ft(-15,50) = 1.3
Value of Fv(-15,50) = -0.15
Step-by-step explanation:
W = perceived temperature
T = actual temperature
W = f( T,V)
Estimate the values of ft ( -15,50) and fv(-15,50)
calculate the Linear approximation of f at(-15,50)
[tex]f_{t}[/tex] (-15,50) = [tex]\lim_{h \to \o}[/tex] [tex]\frac{f(-15+h,40)-f(-15,40)}{h}[/tex]
from the table take h = 5, -5
[tex]f_{t}(-15,40) = \frac{f(-10,40)-f(-15,40)}{5}[/tex] = [tex]\frac{-21+27}{5} = 1.2[/tex]
[tex]f_{t} = \frac{f(-20,40)-f(-15,40)}{-5}[/tex] = 1.4
therefore the average value of [tex]f_{t} (-15,40) = 1.3[/tex]
This means that when the Temperature is -15⁰c and the 40 km/h the value of Ft (-15,40) = 1.3
calculate the linear approximation of
[tex]f_{v} (-15,40) = \lim_{h \to \o} \frac{f(-15,40+h)-f(-15,40)}{h}[/tex]
from the table take h = 10, -10
[tex]f_{v}(-15,40) = \frac{f(-15,50)-f(-15,40)}{10}[/tex] = [tex]\frac{-29+27}{10} = -0.2[/tex]
[tex]f_{v} (-15,40) = \frac{f(-15,30)-f(-15,40)}{-10}[/tex] = [tex]\frac{-26+27}{-10}[/tex] = -0.1
therefore the average value of [tex]f_{v} (-15,40) = -0.15[/tex]
This means that when the temperature = -15⁰c and the wind speed is 40 km/h the temperature will decrease by 0.15⁰c
w = f(T,v)
= -27 + 1.3(T+15) - 0.15(v-40)
= -27 + 1.3T + 19.5 - 0.15v + 6
= 1.3T - 0.15v -1.5
calculate the linear approximation
[tex]\lim_{v \to \infty}[/tex][tex]\frac{dw}{dv} = \lim_{v \to \infty} \frac{d(1.3T-0.15v-1.5)}{dv}[/tex] = -0.15
For the following data set, you are interested to determine the "spread" of the data. Would you employ calculations for the sample standard deviation, or population standard deviation for this data set: You are interested in the heights of students at a particular middle school. Your data set represents the heights of all students in the middle school with 600 students.
Answer: Use calculations for population standard deviation.
Step-by-step explanation:
The population standard deviation is defined as
a parameter which is a fixed valueevaluated by considering individual in the population.A sample standard deviation is defined as
a statistic ( whose value is not fixed ). Evaluated from a subset (sample) of population.Since, data set represents the heights of all students in the middle school with 600 students which is population here.
So, we do calculations to find population standard deviation.
given sin theta=3/5 and 180°<theta<270°, find the following: a. cos(2theta) b. sin(2theta) c. tan(2theta)
I hope this will help uh.....
A jewel box is to be constructed of materials that costs K1 per square inch for the bottom, K2 per square inch for the sides, and K5 per square inch for the top. If the total volume is to be 96 inch cubic, advise Mr Lukonde on what dimensions will minimize the total cost of construction. Show all the calculations.
Answer:
x= 5,77 *∛ K₂ / ( K₁ + K₅ ) the side f the square bottom-top
h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]² heigh of the box
Step-by-step explanation:
Data from problem statement only gives one relation between dimensions of the box, we need two, in order to express surface area as a function of just one variable. In such a case we must assume the box is of square bottom and top.
Then
Area of the bottom A(b) = x² ⇒ C(b) = K₁*x²
Area of the top A(t) = x² ⇒ C(t) = K₅*x²
Total lateral area ( 4 sides) A(l) = 4*x*h ⇒ C(l) = 4*K₂*x*h
V(bx) = 96 in³
V(bx) = x²*h = 96
h = 96/x²
Then total cost as a function of x
C(x) = K₁*x² + K₅*x² + 4*K₂*(96)/x
Taking derivatives on both sides of the equation
C´(x) = 2*K₁*x + 2*K₅*x - 384*K₂/x²
C´(x) = 0 ⇒ 2*K₁*x + 2*K₅*x - 384*K₂/x² = 0
2*K₁*x³ + 2*K₅*x³ = 384*K₂ or K₁*x³ + k₅*x³ = 192*K₂
x³ ( K₁ + K₅ ) = 192*K₂
x = ∛192*K₂ / ( K₁ + K₅ )
x= 5,77 *∛ K₂ / ( K₁ + K₅ )
If we obtain the second derivative
C´´(x) = 2*K₁ + 2*K₅ - (-2*x)*384*K₂/x⁴
C´´(x) = 2*K₁ + 2*K₅ + 768*K₂/x³
As x can not be negative the expression C´´ wil be C´´> 0
then we have a minimum for the function for x = 5,77 *∛ K₂ / ( K₁ + K₅ )
and h = 96 / [ 5,77 *∛ K₂ / ( K₁ + K₅ )]²
h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]²
jogged the track 5/9 miles long and jogged around it 4 times
Answer:
The answer is 2 1/5 miles.
Step-by-step explanation:
You have to multiply 5/9 with 4 since you are going around 4 times. You could also use addition which is 5/9 + 5/9 + 5/9 + 5/9.
Answer:
Hey there!
The person jogged a total of 20/9 miles.
Hope this helps :)
Question 12 of 20 :
Select the best answer for the question.
12. If a number is divisible by both 2 and 3 then we can say the number is divisible by
O A.2.
OB.4.
O C.5.
OD.6.
Mark for review (Will be highlighted on the review page)
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Answer:
The number must be divisible by 6
Step-by-step explanation:
Being divisible by 2 means that 2 is a factor of the number. Same with being divisible by 3, so that means the number has 2 and 3 as factors, therefore, 6 is also a factor, and the number will be divisible by it.
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answer:
I NEED POINTS
Step-by-step explanation:
A building has eight levels above ground and one level below ground. The height of each level from floor to ceiling is feet. What is the net change in elevation going from the floor of the underground level to the ceiling of the fourth level above ground? Assume the floor at ground level is at an elevation of zero feet.
Answer:
72.5 feet
Step-by-step explanation:
The height of each level from floor to ceiling is 14 1/2 feet.
We want to find the net change in elevation going from the floor of the underground level to the ceiling of the 4th level above ground.
In other words, the change in elevation in going 5 floors up.
Each level has a height of 14 1/2 feet (29/2 feet).
Therefore, the height of the fourth level above ground from the underground level will be 5 times the height of one level:
h = 5 * 29/2 = 72.5 feet
The net change in elevation from the floor of the underground level to the 4th level above ground is:
ΔE = [tex]h_4 - h_0[/tex]
[tex]h_0 = 0 feet\\\\h_4 = 72.5 feet[/tex]
Therefore:
ΔE = 72.5 - 0 = 72.5 feet
Answer:
72.5
Step-by-step explanation:
An account is opened with an initial deposit of $100 and earns 3.0% interest compounded monthly. What will the account be worth in 25 years? Round your answer to the nearest dollar.
Answer:
A = $211.50
A = P + I where
P (principal) = $100.00
I (interest) = $111.50
Step-by-step explanation:
$209.37 will the account be worth in 25 years.
What is compound interest?Compound Interest is defined as interest earn on interest.
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
P= $100
r = 3%
t=25 years
substitute the values in formula,
[tex]A = 100(1 + \frac{3}{100})^{25}[/tex]
[tex]A = 100(1 + 0.03)^{25}[/tex]
[tex]A = 100(1.03)^{25}[/tex]
[tex]A=100(2.0937)[/tex]
[tex]A=209.37[/tex]
Hence, $209.37 will the account be worth in 25 years.
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Which of the following best describes an unpredictable event?
Answer:
B. The weather on a particular day a year from now
Step-by-step explanation:
We can only predict the weather in the near future, not long term or all time. The rest of the answer choices are predictable. We will always know the age of a person 10 years from now, we can predict the rating of the movie if we preview and watch it, and if a student studies enough/not enough we can predict the type of grade they will get on a test.
I believe the answer is B since to find the age of a person ten years from now, just add their age by ten. You can predict the rating of an upcoming movie by watching the trailer and seeing if it is good or bad. You can predict the grade a student gets on a test if you know that person is smart or not. You can’t predict weather from a year in the future because anything could happen in a year. This is why I think the answer is B.
The cost of a renting premises is 90% of the total costs of a company. The rental price was reduced 6 times, ceteris parabus. What percentage does the rental cost constitute in the total costs of the company?
Answer:
60%
Step-by-step explanation:
Reducing the rental cost by a factor of 6 makes it be 90%/6 = 15% of the original costs of the company. The non-rental costs are 100% -90% = 10% of the original costs of running the company.
Now, the rental costs are 15%/(15%+10%) = 3/5 of the present costs of the company.
Rental cost constitutes 60% in the total costs of the company.
In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age It was also reported that interviews were conducted on 1, 018 American adults, and that the margin of error was 3% using a 95% confidence level.
a. Verify the margin of error reported by The Marist Poll.
b. Based on a 95% confidence interval, docs the poll provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65?
Answer:
a
The Margin of error is correct
b
No the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 66[/tex]% = 0.66
The sample size is n = 1018
The margin of error is MOE = 3 % = 0.03
The confidence level is C = 95%
Given that the confidence level is 95% , then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level ([tex]1-\alpha[/tex]) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which what we required to calculate the margin of error
Generally the margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{p (1-p )}{n} }[/tex]
substituting values
[tex]MOE = 1.96 * \sqrt{\frac{0.66 (1-66 )}{1018} }[/tex]
[tex]MOE = 0.03[/tex]
[tex]MOE = 3[/tex]%
The 95% is mathematically represented as
[tex]p - MOE < p < p +MOE[/tex]
substituting values
[tex]0.66 -0.03 < p < 0.66 +0.03[/tex]
[tex]0.63 < p < 0.69[/tex]
Looking at the confidence level interval we see that the population proportion is between
63% and 69%
shown that the population proportion is less than 70%
Which means that the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.
The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $2700 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. According to the Central Limit Theorem, which of the following describes the sampling distribution of the sample mean?
a. Normally distributed with a mean of $2700 and a standard deviation of $40
b. Normally distributed with a mean of $2700 and a standard deviation of $400
c. Skewed to the right with a mean of $2700 and a standard deviation of $400
d. Skewed to the right with a mean of $2700 and a standard deviation of $40
Answer:
a. Normally distributed with a mean of $2700 and a standard deviation of $40
Step-by-step explanation:
Given that:
the mean daily revenue is $2700
the standard deviation is $400
sample size n is 100
According to the Central Limit Theorem, the sampling distribution of the sample mean can be computed as follows:
[tex]\mathbf{standard \ deviation =\dfrac{ \sigma}{\sqrt{n}}}[/tex]
standard deviation = [tex]\dfrac{400}{\sqrt{100}}[/tex]
standard deviation = [tex]\dfrac{400}{10}}[/tex]
standard deviation = 40
This is because the sample size n is large ( i,e n > 30) as a result of that the sampling distribution is normally distributed.
Therefore;
the statement that describes the sampling distribution of the sample mean is : option A.
a. Normally distributed with a mean of $2700 and a standard deviation of $40
905,238 In a word form
Answer:
nine hundred five thousand two hundred thirty-eight
help plsssssssssssss
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤
factorize 3x square+5x
Answer:
x(3x+5)
Step-by-step explanation:
3x^2+5x
take out common factor x
= x(3x+5)
Answer:
[tex]x(3x + 5)[/tex]Step-by-step explanation:
3x² + 5x
Factor out X from the expression
= x ( 3x + 5 )
Hope this helps...
Best regards!!
How to calculate a circumference of a circle?
Answer: Pi multiplied by the diameter of the circle
Step-by-step explanation:
Answer:
The formula for finding the circumference of a circle is [tex]C = 2\pi r[/tex]. You substitute the radius of the circle for [tex]r[/tex] and multiply it by [tex]2\pi[/tex].
A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90. its price-earnings ratio equals:
Answer: Price-earnings ratio= 22.0
Step-by-step explanation:
Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90
To find: price-earnings ratio
Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]
Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]
⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]
Hence, the price-earnings ratio= 22.0
(SAT Prep) In the given figure, find x+y. A. 95° B. 205° C. 185° D. 180°
Answer:
I hope it will help you...
The value of [tex]x+y[/tex] will be equal to 185 degrees.
From figure it is observed that,
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
[tex]y=45+60=105[/tex]
We know that, By triangle property sum of all three angles in a triangle must be equal to 180 degrees.
So that, [tex]x+55+45=180[/tex]
[tex]x=180-100=80[/tex]
Thus, [tex]x+y=105+80=185[/tex] degree
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Determine the domain of the function. f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two.
All real numbers except -8, -3, and 2
x ≥ 0
All real numbers
x ≥ -3, x ≠ 2
Answer:
[tex]\huge \boxed{{x\geq -3, \ x \neq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.
[tex]x+8\neq 0[/tex]
Subtract 8 from both parts.
[tex]x\neq -8[/tex]
[tex]x-2\neq 0[/tex]
Add 2 on both parts.
[tex]x\neq 2[/tex]
The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.
[tex]x+3\geq 0[/tex]
Subtract 3 from both parts.
[tex]x\geq -3[/tex]
The domain of the function is [tex]x\geq -3[/tex], [tex]x\neq 2[/tex].
The domain of the given function will be x ≥ -3 and x ≠ 2.
What is the domain of a function?The entire range of independent input variables that can exist is referred to as a function's domain or,
The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.
As per the data given in the question,
The given expression of function is,
f(x) = [tex]\sqrt{\frac{x+3}{(x-8)(x-2)} }[/tex]
The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.
x + 8 ≠ 0
x ≠ -8
And, x - 2 ≠ 0
x ≠ 2
Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.
So,
x + 3 ≥ 0
x ≥ -3
So, the domain of the function will be x ≥ -3 and x ≠ 2.
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verify:
cos(2A)=(cotA-tanA)/cscAsecA
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
cot A = [tex]\frac{cosA}{sinA}[/tex], tanA = [tex]\frac{sinA}{cosA}[/tex], cscA = [tex]\frac{1}{sinA}[/tex], secA = [tex]\frac{1}{cosA}[/tex]
Consider the right side
[tex]\frac{cotA-tanA}{cscAsecA}[/tex]
= [tex]\frac{\frac{cosA}{sinA}-\frac{sinA}{cosA} }{\frac{1}{sinA}.\frac{1}{cosA} }[/tex]
= [tex]\frac{\frac{cos^2A-sin^2A}{sinAcosA} }{\frac{1}{sinAcosA} }[/tex]
= [tex]\frac{cos^2A-sin^2A}{sinAcosA}[/tex] × sinAcosA ( cancel sinAcosA )
= cos²A - sin²A
= cos2A
= left side ⇒ verified
8/7=x/5 what is the value of x round to the nearest tenth
Answer:
x = 5.7Step-by-step explanation:
[tex] \frac{8}{7} = \frac{x}{5} [/tex]
To find x first cross multiply
We have
7x = 8 × 5
7x = 40
Divide both sides by 7
That's
[tex] \frac{7x}{7} = \frac{40}{7} [/tex]
[tex]x = \frac{40}{7} [/tex]
x = 5.7142
We have the final answer as
x = 5.7 to the nearest tenthHope this helps you
Answer:
[tex]\boxed{\sf x = 5.7}[/tex]
Step-by-step explanation:
[tex]\sf \frac{8}{7} = \frac{x}{5} \\=> 1.142 = \frac{x}{5}\\ Multiplying \ both \ sides \ by \ 5\\1.142 * 5 = x\\5.7 = x\\OR\\x = 5.7[/tex]
Find the values of x and y for both questions.
Answer:
16. x=48 y=70
17. x=45 y=5
Step-by-step explanation:
16. This is an isosceles triangle meaning that the two angles are the same. Meaning that (x+7)=55.
55-7=48
(48+7)=55 x=48
There are 180 degrees in a triangle, so 55+55=110
180-110=70. y=70
17. This is a right angled triangle meaning that the squared part is 90 degrees. And it is also an isosceles triangle meaning that x=97.
There are 180 degrees in a triangle, and 90 is already taken, meaning that there is 90 degrees more left.
90/2=45
x=45
9✖️5=45 y=5
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Exhibit 3-3Suppose annual salaries for sales associates from Hayley's Heirlooms have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500.The z-score for a sales associate from this store who earns $37,500 is ____
Answer:
The z-score for a sales associate from this store who earns $37,500 is 2
Step-by-step explanation:
From the given information:
mean [tex]\mu[/tex] = 32500
standard deviation = 2500
Sample mean X = 37500
From the given information;
The value for z can be computed as :
[tex]z= \dfrac{X- \mu}{\sigma}[/tex]
[tex]z= \dfrac{37500- 32500}{2500}[/tex]
[tex]z= \dfrac{5000}{2500}[/tex]
z = 2
The z-score for a sales associate from this store who earns $37,500 is 2
Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The set where p1(t) = t, p2(t) = t2, p3(t) = 2t + 3t2 C: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t + t2
Answer:
The set of vectors A and C are linearly independent.
Step-by-step explanation:
A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} = 0[/tex]
[tex]\alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]
[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]
Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:
[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{1} = -2\cdot k[/tex]
[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{2} = -3\cdot k[/tex]
It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} + \alpha_{3} = 0[/tex]
[tex]3\cdot \alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
The set of vectors A and C are linearly independent.
In order to estimate the difference between the average Miles per Gallon of two different models of automobiles, samples are taken, and the following information is collected. Model A Model B Sample Size 50 55 Sample Mean 32 35 Sample Variance 9 10 a) At 95% confidence develop an interval estimate for the difference between the average Miles per Gallon for the two models. b) Is there conclusive evidence to indicate that one model gets a higher MPG than the other
Answer:
At 95% confidence limits for the true difference between the average Miles per Gallon for the two models is -1.8210 to 4.1789
Yes 95 % confidence means that there's conclusive evidence to indicate that one model gets a higher MPG than the other.
Step-by-step explanation:
Model A Model B
Sample Size 50 55
Sample Mean x` 32 35
Sample Variance s² 9 10
At 95 % confidence limits are given by
x1`-x2` ± 1.96 [tex]\sqrt{\frac{s^{2} }{n1} +\frac{s^{2}}{n2} }[/tex]
Putting the values
32-35 ± 1.96 [tex]\sqrt\frac{9}{50}+\frac{10}{55}[/tex] ( the variance is the square of standard deviation)
-3 ± 1.96 [tex]\sqrt{ \frac{495+500}{2750}[/tex]
-3 ± 1.96( 0.6015)
-3 ± 1.17896
-1.8210; 4.1789
Thus the 95% confidence limits for the true difference between the average Miles per Gallon for the two models is -1.8210 to 4.1789.
Yes 95 % confidence means that there's conclusive evidence to indicate that one model gets a higher MPG than the other.
PLZ CHECK MY ANSWER. Round your answer to the nearest tenth.
I chose D.
A: 72.56 cm^2
B: 80.29 cm^2
C: 60.66 cm^2
D: 70.32 cm^2
Answer:
D. [tex]70.34 cm^2[/tex]
Step-by-step explanation:
Area of sector of a circle is given as θ/360*πr²
Where,
r = radius = 12 cm
θ = 56°
Use 3.14 as π
Plug in the values into the formula and solve
[tex] area = \frac{56}{360}*3.14*12^2 [/tex]
[tex] area = 70.34 [/tex]
Area of the sector ABC = [tex] 70.34 cm^2 [/tex]
The answer is D